My plan is to use the dashboard via a touchscreen connected directly to the pi B+ running node-red, but it seems that when I browse via a laptop, the dashboard is more responsive.
Question: Is it a given that running both a chrome browser and node-red on the same pi will never be as fast as separating these between two pis, even with the network layer is added in?
Well, it rather depends.
But simplistically, if you set up your Pi to have no desktop gui, everything will run a lot faster (except the non-existent desktop of course ).
If you have a laptop, I wouldn't bother with a Pi desktop. You can also save some wiring and keyboard/monitor shenanigans as well. As long as you are reasonably happy with the SSH command line, you don't need the desktop at all and will save a lot of memory and CPU overhead.
Yes as Julian says - running any modern browser on the Pi will be slow compared to almost anywhere else. Only do it if you have to...